Please solve these questions

1. (4 points) Load the burger king data. csv file which contains the Google trends data concerning the query Burger King from 2004 to the present. (a) Estimate the trend function in the data by fitting a parametric curve to the data. Provide a plot of the original data along with the corresponding trend estimate. Also provide a time plot and correlogram of the residuals. Comment on each of these plots. (For correlogram, see acf function in R) (b) Estimate the trend by smoothing (The filter function in R might be helpful). Explain reasons behind your choice of the smoothing parameter. Once again, provide a plot of the original data along with the corresponding trend estimate. Also provide a time plot and correlogram of the residuals. Comment on each of these plots. (c) Difference the data and provide a plot of the differenced data (The diff function in R might be helpful). Is there any trend in the differenced data? Also plot the correlogram of the differenced data and comment on it. (d) Estimate the trend function in the data using isotonic estimation (The isoreg function in R might be helpful). Provide a plot of the original data along with the corresponding trend estimate. Also provide a time plot and correlogram of the residuals. Comment on each of the plots. 2. (5 points) Load the data file football data. csv which contains the google trends data concern- ing the query football from 2004 to the present. (a) Make a time series plot of (yt). Is there any trend or seasonality? (b) Use least squares to fit the following model + 823 cos ( 272t ) + Bas+1 sin ( 27 2it ) ] + wes (1) where (wt) is zero mean white noise. Note that sin(27 (6)/12) = 0, so you have to only estimate (Bo, ..., B12). Plot (yt) and the fitted values on the same graph. lowl The data was ttrained by 2 ag" group Lew age group HL High age group ML The Popular Nevers than one O The non odds ratio is equal to one The Prove modest (greater than ,053 wax human odds ratio is equal to are 2. The Mostations and Epiden logy departments are running a 10K acad save. There are three pairs of runners, in each case, a runner from Miasrat wins matched to s runser from Splat the her from lipl of the tame age. gender and degree of running I paint experience. The difference in each pairs times won takes and a signed rank test performed. matt sig ved ranks pevshe could take! O 0.25 0 0.125 O ars